“The aim of the Imperial College project […] is to create a device that […] does not rely on receiving external signals.”
and
“At the heart of the quantum compass – which could be ready for widespread use in a few years – is a device known as an accelerometer that can measure how an object’s velocity changes”
So, it’s advanced dead reckoning (https://en.wikipedia.org/wiki/Dead_reckoning).
I wonder whether they really don’t use external signals at all or occasionally use them to correct for accumulation of errors. For example, the ability to detect that velocity w.r.t. earth is zero would help with that.
(Of course, for the London subway, the fact that trains tend to follow the tracks can help, if the system knows the track layout. That probably is the simplest way to prevent accumulation of errors, but then, do they really need such a complex accelerometer?)